When you gain muscle, your resting metabolic rate (the number of calories your body burns at rest) does go up. (muscleevo.net)
The above form will calculate your estimated Basal Metabolic Rate, which is the number of calories your body burns at rest. (acaloriecounter.com)
Your BMR is the number of calories that your body burns at rest to do all of the things it needs to do to keep you alive and functioning properly. (acaloriecounter.com)